A298508 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 37, 10, 37, 1, 1, 104, 50, 50, 104, 1, 1, 301, 148, 269, 148, 301, 1, 1, 864, 493, 1297, 1297, 493, 864, 1, 1, 2485, 2093, 6063, 10969, 6063, 2093, 2485, 1, 1, 7144, 8047, 35908, 86979, 86979, 35908, 8047, 7144, 1, 1, 20541, 31951

Offset

1,5

Comments

Table starts

.1....1.....1.......1........1..........1............1.............1

.1....5....12......37......104........301..........864..........2485

.1...12....10......50......148........493.........2093..........8047

.1...37....50.....269.....1297.......6063........35908........203345

.1..104...148....1297....10969......86979.......795788.......7018070

.1..301...493....6063....86979....1091801.....16092678.....225171354

.1..864..2093...35908...795788...16092678....364785216....7961618817

.1.2485..8047..203345..7018070..225171354...7961618817..269830709761

.1.7144.31951.1189795.62968846.3223061387.177727031452.9389112358693

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 5*a(n-2) +8*a(n-3) +4*a(n-4)

k=3: [order 16] for n>18

k=4: [order 58] for n>61

Example

Some solutions for n=5, k=4
..0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..0. .0..1..1..0
..1..1..1..1. .0..0..0..0. .1..1..1..1. .1..0..0..1. .1..1..1..1
..1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..1..1..0. .1..1..1..1. .1..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .1..0..1..1. .0..0..0..0

Crossrefs

Column 2 is A297909.

Sequence in context: A110522 A146987 A297915 * A298328 A299221 A300035

Adjacent sequences: A298505 A298506 A298507 * A298509 A298510 A298511

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 20 2018

Status

approved